Question

what is the prime factorization of 90? 9·10 15·6 2·5·9 2·3·3·5

Explanation:

Step1: Recall Prime Factorization

Prime factorization means expressing a number as a product of prime numbers. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.

Step2: Analyze Each Option

• Option 1: \(9 \cdot 10\). 9 is not a prime number (\(9 = 3 \cdot 3\)) and 10 is not a prime number (\(10 = 2 \cdot 5\)), so this is not a prime factorization.
• Option 2: \(15 \cdot 6\). 15 is not a prime number (\(15 = 3 \cdot 5\)) and 6 is not a prime number (\(6 = 2 \cdot 3\)), so this is not a prime factorization.
• Option 3: \(2 \cdot 5 \cdot 9\). 9 is not a prime number (\(9 = 3 \cdot 3\)), so this is not a prime factorization.
• Option 4: \(2 \cdot 3 \cdot 3 \cdot 5\). All of 2, 3, and 5 are prime numbers. And \(2\times3\times3\times5=90\), so this is the prime factorization of 90.

Answer:

D. \(2 \cdot 3 \cdot 3 \cdot 5\)